What the guy said was, "Do you believe that we should deport the natural born citizen children of illegal immigrants?"
Trick question. There's no such thing.
A Natural Born Citizen is defined as a child born on U.S. soil whose parents are both citizens. This is a qualification beyond just citizenship, and is the crux of the question for Obama.
A secondary point is whether children born on U.S. soil to illegal alien parents are even citizens: they violate the "and subject to the jurisdiction of" clause in the 14th.
So Hunter should have just laughed. The guy hit him with a strawman: he made the conclusion that just because someone is born on U.S. soil that they are "natural born". That's simply not true, on a number of levels.
The jurisdiction means that the US can enforce its laws on them, not that they owe some type of allegience or all the other stupid crap people write. This clause only exempts the children of diplomats who are not under the jurisdiction of the US. When the diplomats wife travels from her embassy which is foreign soil, to the US hospital, pops the kid and then goes back to her foreign soil she is under diplomatic immunity to US law and not under our jurisdiction and therefor her children are not US citizens. Whereas the illegal alien mom has no such immunity. Although she has broken a law and is a criminal her child is still a US citizen. The child of a crack whore is also a US citizen.
If you don't like the law then try to change it.